Subgroups — C₃×#10596031 #13179311

Order 1728.

1876 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#64148	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#64146	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64139	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#64138	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₄×#638	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#3752	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#64107	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#64103	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#64094	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#64093	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#64091	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#64087	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#64085	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#64084	C₂	1	1	yes	maximal, characteristic, complemented
16	#10596031	C₃	1	1	yes	maximal, characteristic, direct product factor
17	C₃×#5560	—	3	4	no	maximal
18	C₂³×C₃×C₃⋊D₃	C₂²	1	1	yes	characteristic
19	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic
20	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
21	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃×#638	C₂²	1	1	yes	characteristic
23	C₂×C₃×#638	C₂²	1	1	yes	characteristic
24	C₂×C₃×#638	C₂²	1	1	yes	characteristic
25	C₂×C₃×#638	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₃×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₃×#634	C₂²	1	1	yes	characteristic, complemented
31	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
32	C₃³×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₃³×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
34	C₃³×C₄²	C₂²	1	1	yes	characteristic, complemented
35	C₃×#3757	C₂²	1	1	yes	characteristic
36	C₃×#3757	C₂²	1	1	yes	characteristic, complemented
37	C₃×#3752	C₂²	1	1	yes	characteristic
38	C₃×#3752	C₂²	1	1	yes	characteristic
39	C₃×#3752	C₂²	1	1	yes	characteristic
40	C₃×#3752	C₂²	1	1	yes	characteristic
41	C₃×#3752	C₂²	1	1	yes	characteristic
42	C₃×#3752	C₂²	1	1	yes	characteristic
43	C₃×#3752	C₂²	1	1	yes	characteristic
44	C₃×#3752	C₂²	1	1	yes	characteristic
45	C₃×#3752	C₂²	1	1	yes	characteristic, complemented
46	C₃×#3752	C₂²	1	1	yes	characteristic, complemented
47	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic, complemented
48	C₃×#3750	C₂²	1	1	yes	characteristic, complemented
49	C₃×#3750	C₂²	1	1	yes	characteristic, complemented
50	C₃×#3750	C₂²	1	1	yes	characteristic, complemented
51	C₃×#3750	C₂²	1	1	yes	characteristic, complemented
52	C₃×C₄×C₃⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
53	C₃²×C₄×D₄	—	2	4	no	—
54	C₃²×C₄×D₄	D₃	1	4	yes	complemented
55	C₃²×C₄×D₄	C₂×C₃	1	1	yes	characteristic, complemented
56	#64148	C₂×C₃	1	1	yes	characteristic, complemented
57	#64146	C₂×C₃	1	1	yes	characteristic, complemented
58	#64139	C₂×C₃	1	1	yes	characteristic, complemented
59	#64138	C₂×C₃	1	1	yes	characteristic, complemented
60	C₄×#638	C₂×C₃	1	1	yes	characteristic, complemented
61	C₂×#3752	C₂×C₃	1	1	yes	characteristic, complemented
62	#64107	C₂×C₃	1	1	yes	characteristic, complemented
63	#64103	C₂×C₃	1	1	yes	characteristic, complemented
64	#64094	C₂×C₃	1	1	yes	characteristic, complemented
65	#64093	C₂×C₃	1	1	yes	characteristic, complemented
66	#64091	C₂×C₃	1	1	yes	characteristic, complemented
67	#64087	C₂×C₃	1	1	yes	characteristic, complemented
68	#64085	C₂×C₃	1	1	yes	characteristic, complemented
69	#64084	C₂×C₃	1	1	yes	characteristic, complemented
70	C₃×#939	—	3	4	no	—
71	C₃×#937	—	3	4	no	—
72	C₃×#930	—	3	4	no	—
73	C₃×#929	—	3	4	no	—
74	C₃×C₄×#67	—	3	4	no	—
75	C₂×C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
76	C₃×#898	—	3	4	no	—
77	C₃×#894	—	3	4	no	—
78	C₃×#885	—	3	4	no	—
79	C₃×#884	—	3	4	no	—
80	C₃×#882	—	3	4	no	—
81	C₃×#878	—	3	4	no	—
82	C₃×#876	—	3	4	no	—
83	C₃×#875	—	3	4	no	—
84	C₂³×C₃³	C₂³	1	1	yes	characteristic
85	C₂³×C₃³	C₂³	1	1	yes	characteristic
86	C₂²×C₃×C₃⋊D₃	—	2	2	no	—
87	C₂²×C₃×C₃⋊D₃	—	4	1	no	—
88	C₂²×C₃×C₃⋊D₃	—	4	1	no	—
89	C₂²×C₃×C₃⋊D₃	C₂³	1	1	yes	characteristic
90	C₂²×C₃×C₃⋊D₃	C₂³	1	1	yes	characteristic
91	C₂²×C₃×C₃⋊D₃	C₂³	1	1	yes	characteristic
92	C₃³×D₄	—	2	2	no	—
93	C₂×C₃³×C₄	—	4	1	no	—
94	C₂×C₃³×C₄	—	4	1	no	—
95	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
96	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
97	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
98	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
99	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
100	C₃×#638	—	2	2	no	—
101	C₃×#638	—	4	1	no	—
102	C₃×#638	—	4	1	no	—
103	C₃×#638	—	4	1	no	—
104	C₂×C₃×C₃⋊Dic₃	—	4	1	no	—
105	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
106	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
107	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
108	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
109	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
110	C₃×C₄⋊(C₃⋊D₃)	—	4	1	no	—
111	C₃×C₄⋊(C₃⋊D₃)	—	4	1	no	—
112	C₃×C₄×C₃⋊D₃	—	4	1	no	—
113	C₃×#634	—	4	1	no	—
114	C₃×#538	—	9	1	no	—
115	#5560	—	3	4	no	—
116	C₂³×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
117	C₂³×C₃×D₃	—	3	4	no	—
118	C₂×C₃²×D₄	—	2	4	no	—
119	C₂×C₃²×D₄	C₂×D₃	1	4	yes	—
120	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
121	C₂²×C₃²×C₄	—	2	4	no	—
122	C₂²×C₃²×C₄	—	2	4	no	—
123	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
124	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	complemented
125	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
126	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic, complemented
127	C₂×#638	C₂²×C₃	1	1	yes	characteristic
128	C₂×#638	C₂²×C₃	1	1	yes	characteristic
129	C₂×#638	C₂²×C₃	1	1	yes	characteristic
130	C₂×#638	C₂²×C₃	1	1	yes	characteristic, complemented
131	C₂²×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
132	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic
133	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic
134	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic, complemented
135	C₂×#634	C₂²×C₃	1	1	yes	characteristic, complemented
136	C₂×C₃×#67	—	3	4	no	—
137	C₂×C₃×#67	—	3	4	no	—
138	C₂×C₃×#67	—	3	4	no	—
139	C₂×C₃×#67	—	3	4	no	—
140	C₂²×C₃×Dic₃	—	3	4	no	—
141	C₂×C₃×D₁₂	—	3	4	no	—
142	C₂×C₃×D₁₂	—	3	4	no	—
143	C₂×C₃×C₄×D₃	—	3	4	no	—
144	C₂×C₃×Dic₆	—	3	4	no	—
145	C₃²×C₄⋊C₄	—	2	4	no	—
146	C₃²×C₄⋊C₄	C₂×D₃	1	4	yes	complemented
147	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
148	C₃²×C₂²⋊C₄	—	2	4	no	—
149	C₃²×C₂²⋊C₄	—	2	4	no	—
150	C₃²×C₂²⋊C₄	C₂×D₃	1	4	yes	—
151	C₃²×C₂²⋊C₄	C₂×D₃	1	4	yes	complemented
152	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
153	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
154	C₃²×C₄²	—	2	4	no	—
155	C₃²×C₄²	C₂×D₃	1	4	yes	complemented
156	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
157	#3757	C₂²×C₃	1	1	yes	characteristic
158	#3757	C₂²×C₃	1	1	yes	characteristic, complemented
159	#3752	C₂²×C₃	1	1	yes	characteristic
160	#3752	C₂²×C₃	1	1	yes	characteristic
161	#3752	C₂²×C₃	1	1	yes	characteristic
162	#3752	C₂²×C₃	1	1	yes	characteristic
163	#3752	C₂²×C₃	1	1	yes	characteristic
164	#3752	C₂²×C₃	1	1	yes	characteristic
165	#3752	C₂²×C₃	1	1	yes	characteristic
166	#3752	C₂²×C₃	1	1	yes	characteristic
167	#3752	C₂²×C₃	1	1	yes	characteristic, complemented
168	#3752	C₂²×C₃	1	1	yes	characteristic, complemented
169	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	1	yes	characteristic, complemented
170	#3750	C₂²×C₃	1	1	yes	characteristic, complemented
171	#3750	C₂²×C₃	1	1	yes	characteristic, complemented
172	#3750	C₂²×C₃	1	1	yes	characteristic, complemented
173	#3750	C₂²×C₃	1	1	yes	characteristic, complemented
174	C₄×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
175	C₃×#217	—	3	4	no	—
176	C₃×#217	—	3	4	no	—
177	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
178	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
179	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
180	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
181	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
182	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
183	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
184	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
185	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
186	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
187	C₃×C₄⋊Dic₃	—	3	4	no	—
188	C₃×Dic₃⋊C₄	—	3	4	no	—
189	C₃×Dic₃⋊C₄	—	3	4	no	—
190	C₃×Dic₃⋊C₄	—	3	4	no	—
191	C₃×Dic₃⋊C₄	—	3	4	no	—
192	C₃×C₄×Dic₃	—	3	4	no	—
193	C₂²×C₃³	—	2	1	no	—
194	C₂²×C₃³	—	2	1	no	—
195	C₂²×C₃³	—	2	1	no	—
196	C₂²×C₃³	—	2	1	no	—
197	C₂²×C₃³	—	2	1	no	—
198	C₂²×C₃³	#41	1	2	yes	—
199	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
200	C₂×C₃×C₃⋊D₃	—	2	1	no	—
201	C₂×C₃×C₃⋊D₃	—	2	1	no	—
202	C₂×C₃×C₃⋊D₃	—	2	1	no	—
203	C₂×C₃×C₃⋊D₃	—	2	1	no	—
204	C₂×C₃×C₃⋊D₃	—	2	1	no	—
205	C₂×C₃×C₃⋊D₃	—	2	1	no	—
206	C₂×C₃×C₃⋊D₃	—	2	1	no	—
207	C₂×C₃×C₃⋊D₃	—	2	1	no	—
208	C₂×C₃×C₃⋊D₃	—	2	1	no	—
209	C₂×C₃×C₃⋊D₃	—	4	4	no	—
210	C₃³×C₄	—	2	1	no	—
211	C₃³×C₄	—	2	1	no	—
212	C₃³×C₄	—	2	1	no	—
213	C₃³×C₄	—	2	1	no	—
214	C₃³×C₄	—	2	1	no	—
215	C₃×C₃⋊Dic₃	—	2	1	no	—
216	C₃×C₃⋊Dic₃	—	2	1	no	—
217	C₃×C₃⋊Dic₃	—	2	1	no	—
218	C₃×C₃⋊Dic₃	—	2	1	no	—
219	C₃×C₃⋊Dic₃	—	2	1	no	—
220	C₃×#126	—	9	1	no	—
221	C₃×#126	—	9	1	no	—
222	C₃×#124	—	9	1	no	—
223	C₃×#124	—	9	1	no	—
224	C₃×#123	—	9	1	no	—
225	C₃×#123	—	9	1	no	—
226	C₃×C₂²⋊Q₈	—	9	1	no	—
227	C₃×#121	—	9	1	no	—
228	C₃×#121	—	9	1	no	—
229	C₃×#121	—	9	1	no	—
230	C₃×#120	—	9	1	no	—
231	C₃×#120	—	9	1	no	—
232	C₃×C₄×D₄	—	2	4	no	—
233	C₃×C₄×D₄	—	9	1	no	—
234	C₃×C₄×D₄	C₃×D₃	1	4	yes	complemented
235	C₃×C₄×D₄	C₃⋊D₃	1	1	yes	characteristic, complemented
236	C₂×C₃×C₂²⋊C₄	—	9	1	no	—
237	#939	—	3	4	no	—
238	#937	—	3	4	no	—
239	#930	—	3	4	no	—
240	#929	—	3	4	no	—
241	C₄×#67	—	3	4	no	—
242	C₂×(C₂×D₃)⋊C₄	—	3	4	no	—
243	#898	—	3	4	no	—
244	#894	—	3	4	no	—
245	#885	—	3	4	no	—
246	#884	—	3	4	no	—
247	#882	—	3	4	no	—
248	#878	—	3	4	no	—
249	#876	—	3	4	no	—
250	#875	—	3	4	no	—
251	C₂³×C₃²	—	2	4	no	—
252	C₂³×C₃²	—	2	4	no	—
253	C₂³×C₃²	C₂²×D₃	1	4	yes	—
254	C₂³×C₃²	C₂²×D₃	1	4	yes	—
255	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
256	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
257	C₂²×C₃⋊D₃	—	2	2	no	—
258	C₂²×C₃⋊D₃	—	4	1	no	—
259	C₂²×C₃⋊D₃	—	4	1	no	—
260	C₂²×C₃⋊D₃	C₂³×C₃	1	1	yes	characteristic
261	C₂²×C₃⋊D₃	C₂³×C₃	1	1	yes	characteristic
262	C₂²×C₃⋊D₃	C₂³×C₃	1	1	yes	characteristic
263	C₂²×C₃×D₃	—	3	4	no	—
264	C₂²×C₃×D₃	—	3	4	no	—
265	C₂²×C₃×D₃	—	3	4	no	—
266	C₂²×C₃×D₃	—	6	8	no	—
267	C₂²×C₃×D₃	—	12	4	no	—
268	C₂²×C₃×D₃	—	12	4	no	—
269	C₃²×D₄	—	2	16	no	—
270	C₃²×D₄	—	2	8	no	—
271	C₃²×D₄	—	2	2	no	—
272	C₂×C₃²×C₄	—	2	4	no	—
273	C₂×C₃²×C₄	—	2	4	no	—
274	C₂×C₃²×C₄	—	2	4	no	—
275	C₂×C₃²×C₄	—	2	4	no	—
276	C₂×C₃²×C₄	—	2	4	no	—
277	C₂×C₃²×C₄	—	4	4	no	—
278	C₂×C₃²×C₄	—	4	4	no	—
279	C₂×C₃²×C₄	—	4	1	no	—
280	C₂×C₃²×C₄	—	4	1	no	—
281	C₂×C₃²×C₄	—	4	8	no	—
282	C₂×C₃²×C₄	—	4	8	no	—
283	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
284	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
285	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
286	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
287	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
288	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
289	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
290	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
291	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
292	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
293	#638	—	2	2	no	—
294	#638	—	4	1	no	—
295	#638	—	4	1	no	—
296	#638	—	4	1	no	—
297	C₂×C₃⋊Dic₃	—	4	1	no	—
298	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
299	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
300	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
301	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
302	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
303	C₄⋊(C₃⋊D₃)	—	4	1	no	—
304	C₄⋊(C₃⋊D₃)	—	4	1	no	—
305	C₄×C₃⋊D₃	—	4	1	no	—
306	#634	—	4	1	no	—
307	C₃×#67	—	6	8	no	—
308	C₃×#67	—	12	4	no	—
309	C₃×#67	—	12	4	no	—
310	C₃×#67	—	12	4	no	—
311	C₂×C₃×Dic₃	—	3	4	no	—
312	C₂×C₃×Dic₃	—	3	4	no	—
313	C₂×C₃×Dic₃	—	3	4	no	—
314	C₂×C₃×Dic₃	—	3	4	no	—
315	C₂×C₃×Dic₃	—	3	4	no	—
316	C₂×C₃×Dic₃	—	12	4	no	—
317	C₃×D₁₂	—	12	4	no	—
318	C₃×D₁₂	—	12	4	no	—
319	C₃×C₄×D₃	—	12	4	no	—
320	C₃×Dic₆	—	12	4	no	—
321	#538	—	9	1	no	Sylow
322	C₂×C₃³	—	2	2	no	—
323	C₂×C₃³	—	4	1	no	—
324	C₂×C₃³	C₂×#41	1	1	yes	characteristic
325	C₂×C₃³	H(5,𝔽₂)	1	1	yes	characteristic
326	C₂×C₃³	H(5,𝔽₂)	1	1	yes	characteristic
327	C₃×C₃⋊D₃	—	4	1	no	—
328	C₃×C₃⋊D₃	—	4	1	no	—
329	C₃×C₃⋊D₃	—	4	1	no	—
330	C₂⁴×C₃	—	9	1	no	—
331	C₂³×D₃	—	3	4	no	—
332	C₂×C₃×Q₈	—	9	1	no	—
333	C₂×C₃×D₄	—	2	4	no	—
334	C₂×C₃×D₄	—	9	1	no	—
335	C₂×C₃×D₄	—	9	1	no	—
336	C₂×C₃×D₄	—	9	1	no	—
337	C₂×C₃×D₄	—	9	1	no	—
338	C₂×C₃×D₄	—	9	1	no	—
339	C₂×C₃×D₄	—	9	1	no	—
340	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	—
341	C₂×C₃×D₄	C₂×C₃⋊D₃	1	1	yes	characteristic
342	C₂²×C₃×C₄	—	2	4	no	—
343	C₂²×C₃×C₄	—	2	4	no	—
344	C₂²×C₃×C₄	—	9	1	no	—
345	C₂²×C₃×C₄	—	9	1	no	—
346	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
347	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	complemented
348	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
349	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
350	C₂×#67	—	3	4	no	—
351	C₂×#67	—	3	4	no	—
352	C₂×#67	—	3	4	no	—
353	C₂×#67	—	3	4	no	—
354	C₂²×Dic₃	—	3	4	no	—
355	C₂×D₁₂	—	3	4	no	—
356	C₂×D₁₂	—	3	4	no	—
357	C₂×C₄×D₃	—	3	4	no	—
358	C₂×Dic₆	—	3	4	no	—
359	C₃×C₄⋊C₄	—	2	4	no	—
360	C₃×C₄⋊C₄	—	9	1	no	—
361	C₃×C₄⋊C₄	—	9	1	no	—
362	C₃×C₄⋊C₄	—	9	1	no	—
363	C₃×C₄⋊C₄	—	9	1	no	—
364	C₃×C₄⋊C₄	—	9	1	no	—
365	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	complemented
366	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
367	C₃×C₂²⋊C₄	—	2	4	no	—
368	C₃×C₂²⋊C₄	—	2	4	no	—
369	C₃×C₂²⋊C₄	—	9	1	no	—
370	C₃×C₂²⋊C₄	—	9	1	no	—
371	C₃×C₂²⋊C₄	—	9	1	no	—
372	C₃×C₂²⋊C₄	—	9	1	no	—
373	C₃×C₂²⋊C₄	—	9	1	no	—
374	C₃×C₂²⋊C₄	—	9	1	no	—
375	C₃×C₂²⋊C₄	—	9	1	no	—
376	C₃×C₂²⋊C₄	—	9	1	no	—
377	C₃×C₂²⋊C₄	—	9	1	no	—
378	C₃×C₂²⋊C₄	—	9	1	no	—
379	C₃×C₂²⋊C₄	—	9	1	no	—
380	C₃×C₂²⋊C₄	—	9	1	no	—
381	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	4	yes	—
382	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	4	yes	complemented
383	C₃×C₂²⋊C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
384	C₃×C₂²⋊C₄	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
385	C₃×C₄²	—	2	4	no	—
386	C₃×C₄²	—	9	1	no	—
387	C₃×C₄²	C₂×C₃×D₃	1	4	yes	complemented
388	C₃×C₄²	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
389	#217	—	3	4	no	—
390	#217	—	3	4	no	—
391	(C₂×D₃)⋊C₄	—	3	4	no	—
392	(C₂×D₃)⋊C₄	—	3	4	no	—
393	(C₂×D₃)⋊C₄	—	3	4	no	—
394	(C₂×D₃)⋊C₄	—	3	4	no	—
395	(C₂×D₃)⋊C₄	—	3	4	no	—
396	(C₂×D₃)⋊C₄	—	3	4	no	—
397	(C₂×D₃)⋊C₄	—	3	4	no	—
398	(C₂×D₃)⋊C₄	—	3	4	no	—
399	(C₂×D₃)⋊C₄	—	3	4	no	—
400	(C₂×D₃)⋊C₄	—	3	4	no	—
401	C₄⋊Dic₃	—	3	4	no	—
402	Dic₃⋊C₄	—	3	4	no	—
403	Dic₃⋊C₄	—	3	4	no	—
404	Dic₃⋊C₄	—	3	4	no	—
405	Dic₃⋊C₄	—	3	4	no	—
406	C₄×Dic₃	—	3	4	no	—
407	C₂²×C₃²	—	2	1	no	—
408	C₂²×C₃²	—	2	1	no	—
409	C₂²×C₃²	—	2	8	no	—
410	C₂²×C₃²	—	2	4	no	—
411	C₂²×C₃²	—	2	1	no	—
412	C₂²×C₃²	—	2	1	no	—
413	C₂²×C₃²	—	2	1	no	—
414	C₂²×C₃²	—	2	4	no	—
415	C₂²×C₃²	—	2	8	no	—
416	C₂²×C₃²	—	2	4	no	—
417	C₂²×C₃²	—	2	4	no	—
418	C₂²×C₃²	—	2	4	no	—
419	C₂²×C₃²	—	2	4	no	—
420	C₂²×C₃²	—	4	4	no	—
421	C₂²×C₃²	—	4	4	no	—
422	C₂²×C₃²	—	4	4	no	—
423	C₂²×C₃²	—	4	4	no	—
424	C₂²×C₃²	#235	1	8	yes	—
425	C₂²×C₃²	C₃×#41	1	2	yes	—
426	C₂²×C₃²	C₂³×D₃	1	4	yes	—
427	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
428	C₂×C₃⋊D₃	—	2	1	no	—
429	C₂×C₃⋊D₃	—	2	1	no	—
430	C₂×C₃⋊D₃	—	2	1	no	—
431	C₂×C₃⋊D₃	—	2	1	no	—
432	C₂×C₃⋊D₃	—	2	1	no	—
433	C₂×C₃⋊D₃	—	2	1	no	—
434	C₂×C₃⋊D₃	—	2	1	no	—
435	C₂×C₃⋊D₃	—	2	1	no	—
436	C₂×C₃⋊D₃	—	2	1	no	—
437	C₂×C₃⋊D₃	—	4	4	no	—
438	C₂×C₃×D₃	—	6	4	no	—
439	C₂×C₃×D₃	—	6	4	no	—
440	C₂×C₃×D₃	—	6	4	no	—
441	C₂×C₃×D₃	—	6	4	no	—
442	C₂×C₃×D₃	—	6	4	no	—
443	C₂×C₃×D₃	—	6	4	no	—
444	C₂×C₃×D₃	—	6	4	no	—
445	C₂×C₃×D₃	—	6	4	no	—
446	C₂×C₃×D₃	—	6	4	no	—
447	C₂×C₃×D₃	—	12	16	no	—
448	C₃²×C₄	—	2	8	no	—
449	C₃²×C₄	—	2	8	no	—
450	C₃²×C₄	—	2	4	no	—
451	C₃²×C₄	—	2	4	no	—
452	C₃²×C₄	—	2	1	no	—
453	C₃²×C₄	—	2	1	no	—
454	C₃²×C₄	—	2	1	no	—
455	C₃²×C₄	—	2	1	no	—
456	C₃²×C₄	—	2	1	no	—
457	C₃²×C₄	—	2	4	no	—
458	C₃²×C₄	—	2	4	no	—
459	C₃²×C₄	—	2	4	no	—
460	C₃²×C₄	—	4	4	no	—
461	C₃²×C₄	—	4	4	no	—
462	C₃²×C₄	—	4	4	no	—
463	C₃⋊Dic₃	—	2	1	no	—
464	C₃⋊Dic₃	—	2	1	no	—
465	C₃⋊Dic₃	—	2	1	no	—
466	C₃⋊Dic₃	—	2	1	no	—
467	C₃⋊Dic₃	—	2	1	no	—
468	C₃×Dic₃	—	6	4	no	—
469	C₃×Dic₃	—	6	4	no	—
470	C₃×Dic₃	—	6	4	no	—
471	C₃×Dic₃	—	6	4	no	—
472	C₃×Dic₃	—	6	4	no	—
473	#126	—	9	1	no	—
474	#126	—	9	1	no	—
475	#124	—	9	1	no	—
476	#124	—	9	1	no	—
477	#123	—	9	1	no	—
478	#123	—	9	1	no	—
479	C₂²⋊Q₈	—	9	1	no	—
480	#121	—	9	1	no	—
481	#121	—	9	1	no	—
482	#121	—	9	1	no	—
483	#120	—	9	1	no	—
484	#120	—	9	1	no	—
485	C₄×D₄	—	9	1	no	—
486	C₄×D₄	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
487	C₂×C₂²⋊C₄	—	9	1	no	—
488	C₃³	#538	1	1	yes	characteristic, complemented, Sylow
489	C₂³×C₃	—	2	4	no	—
490	C₂³×C₃	—	2	4	no	—
491	C₂³×C₃	—	9	1	no	—
492	C₂³×C₃	—	9	1	no	—
493	C₂³×C₃	—	9	1	no	—
494	C₂³×C₃	—	18	2	no	—
495	C₂³×C₃	—	36	1	no	—
496	C₂³×C₃	—	36	1	no	—
497	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
498	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
499	C₂³×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
500	C₂³×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
501	C₂²×D₃	—	3	4	no	—
502	C₂²×D₃	—	3	4	no	—
503	C₂²×D₃	—	3	4	no	—
504	C₂²×D₃	—	6	8	no	—
505	C₂²×D₃	—	12	4	no	—
506	C₂²×D₃	—	12	4	no	—
507	C₃×Q₈	—	36	1	no	—
508	C₃×D₄	—	2	16	no	—
509	C₃×D₄	—	2	8	no	—
510	C₃×D₄	—	2	2	no	—
511	C₃×D₄	—	18	2	no	—
512	C₃×D₄	—	36	1	no	—
513	C₃×D₄	—	36	1	no	—
514	C₃×D₄	—	36	1	no	—
515	C₃×D₄	—	36	1	no	—
516	C₃×D₄	—	36	1	no	—
517	C₂×C₃×C₄	—	2	4	no	—
518	C₂×C₃×C₄	—	2	4	no	—
519	C₂×C₃×C₄	—	2	4	no	—
520	C₂×C₃×C₄	—	2	4	no	—
521	C₂×C₃×C₄	—	2	4	no	—
522	C₂×C₃×C₄	—	4	4	no	—
523	C₂×C₃×C₄	—	4	4	no	—
524	C₂×C₃×C₄	—	4	1	no	—
525	C₂×C₃×C₄	—	4	1	no	—
526	C₂×C₃×C₄	—	4	8	no	—
527	C₂×C₃×C₄	—	4	8	no	—
528	C₂×C₃×C₄	—	9	1	no	—
529	C₂×C₃×C₄	—	9	1	no	—
530	C₂×C₃×C₄	—	9	1	no	—
531	C₂×C₃×C₄	—	9	1	no	—
532	C₂×C₃×C₄	—	9	1	no	—
533	C₂×C₃×C₄	—	36	1	no	—
534	C₂×C₃×C₄	—	36	1	no	—
535	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
536	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
537	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
538	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
539	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
540	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
541	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
542	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
543	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
544	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
545	#67	—	6	8	no	—
546	#67	—	12	4	no	—
547	#67	—	12	4	no	—
548	#67	—	12	4	no	—
549	C₂×Dic₃	—	3	4	no	—
550	C₂×Dic₃	—	3	4	no	—
551	C₂×Dic₃	—	3	4	no	—
552	C₂×Dic₃	—	3	4	no	—
553	C₂×Dic₃	—	3	4	no	—
554	C₂×Dic₃	—	12	4	no	—
555	D₁₂	—	12	4	no	—
556	D₁₂	—	12	4	no	—
557	C₄×D₃	—	12	4	no	—
558	Dic₆	—	12	4	no	—
559	C₂×C₃²	—	2	2	no	—
560	C₂×C₃²	—	2	4	no	—
561	C₂×C₃²	—	2	4	no	—
562	C₂×C₃²	—	2	4	no	—
563	C₂×C₃²	—	2	8	no	—
564	C₂×C₃²	—	4	8	no	—
565	C₂×C₃²	—	4	8	no	—
566	C₂×C₃²	—	4	4	no	—
567	C₂×C₃²	—	4	1	no	—
568	C₂×C₃²	C₂×#235	1	4	yes	—
569	C₂×C₃²	#1004	1	4	yes	—
570	C₂×C₃²	#1009	1	4	yes	—
571	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
572	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
573	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
574	C₃⋊D₃	—	4	1	no	—
575	C₃⋊D₃	—	4	1	no	—
576	C₃⋊D₃	—	4	1	no	—
577	C₃×D₃	—	12	4	no	—
578	C₃×D₃	—	12	4	no	—
579	C₃×D₃	—	12	4	no	—
580	C₂⁴	—	9	1	no	—
581	C₂×Q₈	—	9	1	no	—
582	C₂×D₄	—	9	1	no	—
583	C₂×D₄	—	9	1	no	—
584	C₂×D₄	—	9	1	no	—
585	C₂×D₄	—	9	1	no	—
586	C₂×D₄	—	9	1	no	—
587	C₂×D₄	—	9	1	no	—
588	C₂×D₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
589	C₂²×C₄	—	9	1	no	—
590	C₂²×C₄	—	9	1	no	—
591	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
592	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
593	C₄⋊C₄	—	9	1	no	—
594	C₄⋊C₄	—	9	1	no	—
595	C₄⋊C₄	—	9	1	no	—
596	C₄⋊C₄	—	9	1	no	—
597	C₄⋊C₄	—	9	1	no	—
598	C₄⋊C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
599	C₂²⋊C₄	—	9	1	no	—
600	C₂²⋊C₄	—	9	1	no	—
601	C₂²⋊C₄	—	9	1	no	—
602	C₂²⋊C₄	—	9	1	no	—
603	C₂²⋊C₄	—	9	1	no	—
604	C₂²⋊C₄	—	9	1	no	—
605	C₂²⋊C₄	—	9	1	no	—
606	C₂²⋊C₄	—	9	1	no	—
607	C₂²⋊C₄	—	9	1	no	—
608	C₂²⋊C₄	—	9	1	no	—
609	C₂²⋊C₄	—	9	1	no	—
610	C₂²⋊C₄	—	9	1	no	—
611	C₂²⋊C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
612	C₂²⋊C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
613	C₄²	—	9	1	no	—
614	C₄²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
615	C₂²×C₃	—	2	4	no	—
616	C₂²×C₃	—	2	4	no	—
617	C₂²×C₃	—	2	1	no	—
618	C₂²×C₃	—	2	1	no	—
619	C₂²×C₃	—	2	8	no	—
620	C₂²×C₃	—	2	4	no	—
621	C₂²×C₃	—	2	4	no	—
622	C₂²×C₃	—	2	4	no	—
623	C₂²×C₃	—	2	1	no	—
624	C₂²×C₃	—	2	1	no	—
625	C₂²×C₃	—	2	1	no	—
626	C₂²×C₃	—	2	4	no	—
627	C₂²×C₃	—	2	8	no	—
628	C₂²×C₃	—	4	4	no	—
629	C₂²×C₃	—	4	4	no	—
630	C₂²×C₃	—	4	4	no	—
631	C₂²×C₃	—	4	4	no	—
632	C₂²×C₃	—	18	1	no	—
633	C₂²×C₃	—	18	1	no	—
634	C₂²×C₃	—	18	1	no	—
635	C₂²×C₃	—	18	1	no	—
636	C₂²×C₃	—	18	1	no	—
637	C₂²×C₃	—	18	1	no	—
638	C₂²×C₃	—	18	1	no	—
639	C₂²×C₃	—	18	1	no	—
640	C₂²×C₃	—	18	1	no	—
641	C₂²×C₃	—	36	4	no	—
642	C₂²×C₃	C₃×#235	1	8	yes	—
643	C₂²×C₃	#3828	1	2	yes	—
644	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
645	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
646	C₂×D₃	—	6	4	no	—
647	C₂×D₃	—	6	4	no	—
648	C₂×D₃	—	6	4	no	—
649	C₂×D₃	—	6	4	no	—
650	C₂×D₃	—	6	4	no	—
651	C₂×D₃	—	6	4	no	—
652	C₂×D₃	—	6	4	no	—
653	C₂×D₃	—	6	4	no	—
654	C₂×D₃	—	6	4	no	—
655	C₂×D₃	—	12	16	no	—
656	C₃×C₄	—	2	8	no	—
657	C₃×C₄	—	2	8	no	—
658	C₃×C₄	—	2	4	no	—
659	C₃×C₄	—	2	4	no	—
660	C₃×C₄	—	2	4	no	—
661	C₃×C₄	—	2	4	no	—
662	C₃×C₄	—	2	4	no	—
663	C₃×C₄	—	2	1	no	—
664	C₃×C₄	—	2	1	no	—
665	C₃×C₄	—	2	1	no	—
666	C₃×C₄	—	2	1	no	—
667	C₃×C₄	—	2	1	no	—
668	C₃×C₄	—	4	4	no	—
669	C₃×C₄	—	4	4	no	—
670	C₃×C₄	—	4	4	no	—
671	C₃×C₄	—	18	1	no	—
672	C₃×C₄	—	18	1	no	—
673	C₃×C₄	—	18	1	no	—
674	C₃×C₄	—	18	1	no	—
675	C₃×C₄	—	18	1	no	—
676	Dic₃	—	6	4	no	—
677	Dic₃	—	6	4	no	—
678	Dic₃	—	6	4	no	—
679	Dic₃	—	6	4	no	—
680	Dic₃	—	6	4	no	—
681	C₃²	—	2	4	no	—
682	C₃²	#5560	1	4	yes	complemented
683	C₃²	C₃×#538	1	1	yes	characteristic, complemented
684	C₂³	—	9	1	no	—
685	C₂³	—	9	1	no	—
686	C₂³	—	9	1	no	—
687	C₂³	—	18	2	no	—
688	C₂³	—	36	1	no	—
689	C₂³	—	36	1	no	—
690	C₂³	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
691	C₂³	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
692	Q₈	—	36	1	no	—
693	D₄	—	2	2	no	—
694	D₄	—	18	2	no	—
695	D₄	—	36	1	no	—
696	D₄	—	36	1	no	—
697	D₄	—	36	1	no	—
698	D₄	—	36	1	no	—
699	D₄	—	36	1	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	4	1	no	—
702	C₂×C₄	—	9	1	no	—
703	C₂×C₄	—	9	1	no	—
704	C₂×C₄	—	9	1	no	—
705	C₂×C₄	—	9	1	no	—
706	C₂×C₄	—	9	1	no	—
707	C₂×C₄	—	36	1	no	—
708	C₂×C₄	—	36	1	no	—
709	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
710	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
711	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
712	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
713	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
714	C₂×C₃	—	2	8	no	—
715	C₂×C₃	—	2	2	no	—
716	C₂×C₃	—	2	4	no	—
717	C₂×C₃	—	2	4	no	—
718	C₂×C₃	—	2	4	no	—
719	C₂×C₃	—	4	8	no	—
720	C₂×C₃	—	4	8	no	—
721	C₂×C₃	—	4	4	no	—
722	C₂×C₃	—	4	1	no	—
723	C₂×C₃	—	36	1	no	—
724	C₂×C₃	—	36	1	no	—
725	C₂×C₃	—	36	1	no	—
726	C₂×C₃	C₂×C₃×#235	1	4	yes	—
727	C₂×C₃	C₃×#1004	1	4	yes	—
728	C₂×C₃	C₃×#1009	1	4	yes	—
729	C₂×C₃	C₂×#3828	1	1	yes	characteristic
730	C₂×C₃	#64361	1	1	yes	characteristic
731	C₂×C₃	#64366	1	1	yes	characteristic
732	D₃	—	12	4	no	—
733	D₃	—	12	4	no	—
734	D₃	—	12	4	no	—
735	C₂²	—	2	1	no	—
736	C₂²	—	2	1	no	—
737	C₂²	—	2	1	no	—
738	C₂²	—	2	1	no	—
739	C₂²	—	2	1	no	—
740	C₂²	—	18	1	no	—
741	C₂²	—	18	1	no	—
742	C₂²	—	18	1	no	—
743	C₂²	—	18	1	no	—
744	C₂²	—	18	1	no	—
745	C₂²	—	18	1	no	—
746	C₂²	—	18	1	no	—
747	C₂²	—	18	1	no	—
748	C₂²	—	18	1	no	—
749	C₂²	—	36	4	no	—
750	C₂²	C₃×#3828	1	2	yes	—
751	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
752	C₄	—	2	1	no	—
753	C₄	—	2	1	no	—
754	C₄	—	2	1	no	—
755	C₄	—	2	1	no	—
756	C₄	—	2	1	no	—
757	C₄	—	18	1	no	—
758	C₄	—	18	1	no	—
759	C₄	—	18	1	no	—
760	C₄	—	18	1	no	—
761	C₄	—	18	1	no	—
762	C₃	—	2	4	no	—
763	C₃	C₃×#5560	1	4	yes	complemented
764	C₃	#10596031	1	1	yes	characteristic, direct product factor
765	C₂	—	2	2	no	—
766	C₂	—	4	1	no	—
767	C₂	—	36	1	no	—
768	C₂	—	36	1	no	—
769	C₂	—	36	1	no	—
770	C₂	C₂×C₃×#3828	1	1	yes	characteristic
771	C₂	C₃×#64361	1	1	yes	characteristic
772	C₂	C₃×#64366	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×C₃⋊D₃
commutator, cosocle	C₂²×C₃²	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×C₃⋊D₃
Fitting	C₃³×C₄×D₄	C₂
socle	C₂²×C₃³	C₂⁴
hypercenter	C₃×C₄×D₄	C₃⋊D₃
hypocenter	C₃²	C₃×#538
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×D₄

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃³×C₄×D₄	C₂	semidirect
2. C₃×#64148	C₂	semidirect
3. C₃×#64146	C₂	semidirect
4. C₃×#64139	C₂	semidirect
5. C₃×#64138	C₂	semidirect
6. C₃×C₄×#638	C₂	semidirect
7. C₂×C₃×#3752	C₂	semidirect
8. C₃×#64107	C₂	semidirect
9. C₃×#64103	C₂	semidirect
10. C₃×#64094	C₂	semidirect
11. C₃×#64093	C₂	semidirect
12. C₃×#64091	C₂	semidirect
13. C₃×#64087	C₂	semidirect
14. C₃×#64085	C₂	semidirect
15. C₃×#64084	C₂	semidirect
16. #10596031	C₃	direct (N × H)
21. C₂²×C₃³×C₄	C₂²	semidirect
25. C₂×C₃×#638	C₂²	semidirect
29. C₂×C₃×C₄×C₃⋊D₃	C₂²	semidirect
30. C₂×C₃×#634	C₂²	semidirect
31. C₃³×C₄⋊C₄	C₂²	semidirect
33. C₃³×C₂²⋊C₄	C₂²	semidirect
34. C₃³×C₄²	C₂²	semidirect
36. C₃×#3757	C₂²	semidirect
45. C₃×#3752	C₂²	semidirect
46. C₃×#3752	C₂²	semidirect
47. C₃×C₄⋊(C₃⋊Dic₃)	C₂²	semidirect
48. C₃×#3750	C₂²	semidirect
49. C₃×#3750	C₂²	semidirect
50. C₃×#3750	C₂²	semidirect
51. C₃×#3750	C₂²	semidirect
52. C₃×C₄×C₃⋊Dic₃	C₂²	semidirect
54. C₃²×C₄×D₄	D₃	semidirect
55. C₃²×C₄×D₄	C₂×C₃	semidirect
56. #64148	C₂×C₃	semidirect
57. #64146	C₂×C₃	semidirect
58. #64139	C₂×C₃	semidirect
59. #64138	C₂×C₃	semidirect
60. C₄×#638	C₂×C₃	semidirect
61. C₂×#3752	C₂×C₃	semidirect
62. #64107	C₂×C₃	semidirect
63. #64103	C₂×C₃	semidirect
64. #64094	C₂×C₃	semidirect
65. #64093	C₂×C₃	semidirect
66. #64091	C₂×C₃	semidirect
67. #64087	C₂×C₃	semidirect
68. #64085	C₂×C₃	semidirect
69. #64084	C₂×C₃	semidirect
124. C₂²×C₃²×C₄	C₂×D₃	semidirect
126. C₂²×C₃²×C₄	C₂²×C₃	semidirect
130. C₂×#638	C₂²×C₃	semidirect
134. C₂×C₄×C₃⋊D₃	C₂²×C₃	semidirect
135. C₂×#634	C₂²×C₃	semidirect
146. C₃²×C₄⋊C₄	C₂×D₃	semidirect
147. C₃²×C₄⋊C₄	C₂²×C₃	semidirect
151. C₃²×C₂²⋊C₄	C₂×D₃	semidirect
153. C₃²×C₂²⋊C₄	C₂²×C₃	semidirect
155. C₃²×C₄²	C₂×D₃	semidirect
156. C₃²×C₄²	C₂²×C₃	semidirect
158. #3757	C₂²×C₃	semidirect
167. #3752	C₂²×C₃	semidirect
168. #3752	C₂²×C₃	semidirect
169. C₄⋊(C₃⋊Dic₃)	C₂²×C₃	semidirect
170. #3750	C₂²×C₃	semidirect
171. #3750	C₂²×C₃	semidirect
172. #3750	C₂²×C₃	semidirect
173. #3750	C₂²×C₃	semidirect
174. C₄×C₃⋊Dic₃	C₂²×C₃	semidirect
234. C₃×C₄×D₄	C₃×D₃	semidirect
235. C₃×C₄×D₄	C₃⋊D₃	semidirect
347. C₂²×C₃×C₄	C₂×C₃×D₃	semidirect
349. C₂²×C₃×C₄	C₂×C₃⋊D₃	semidirect
365. C₃×C₄⋊C₄	C₂×C₃×D₃	semidirect
366. C₃×C₄⋊C₄	C₂×C₃⋊D₃	semidirect
382. C₃×C₂²⋊C₄	C₂×C₃×D₃	semidirect
384. C₃×C₂²⋊C₄	C₂×C₃⋊D₃	semidirect
387. C₃×C₄²	C₂×C₃×D₃	semidirect
388. C₃×C₄²	C₂×C₃⋊D₃	semidirect
486. C₄×D₄	C₃×C₃⋊D₃	semidirect
488. C₃³	#538	semidirect
592. C₂²×C₄	C₂×C₃×C₃⋊D₃	semidirect
598. C₄⋊C₄	C₂×C₃×C₃⋊D₃	semidirect
612. C₂²⋊C₄	C₂×C₃×C₃⋊D₃	semidirect
614. C₄²	C₂×C₃×C₃⋊D₃	semidirect
682. C₃²	#5560	semidirect
683. C₃²	C₃×#538	semidirect
763. C₃	C₃×#5560	semidirect
764. C₃	#10596031	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃³×C₄×D₄	2
C₃×#64148	2
C₃×#64146	2
C₃×#64139	2
C₃×#64138	2
C₃×C₄×#638	2
C₂×C₃×#3752	2
C₃×#64107	2
C₃×#64103	2
C₃×#64094	2
C₃×#64093	2
C₃×#64091	2
C₃×#64087	2
C₃×#64085	2
C₃×#64084	2
#10596031	3
C₃×#5560	3

Subgroups — C3×#10596031 #13179311

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10596031 #13179311